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<H2> Table of Contents
</H2>

<PRE>
   <A HREF="#SCLK Required Reading">SCLK Required Reading</A>
      <A HREF="#Abstract">Abstract</A>
      <A HREF="#Introduction">Introduction</A>
         <A HREF="#References">References</A>
         <A HREF="#Support for New Missions">Support for New Missions</A>
         <A HREF="#Detection of Non-native Text Files">Detection of Non-native Text Files</A>
      <A HREF="#The Basics">The Basics</A>
         <A HREF="#SCLK rates">SCLK rates</A>
         <A HREF="#SCLK kernels">SCLK kernels</A>
         <A HREF="#Partitions, briefly">Partitions, briefly</A>
         <A HREF="#Converting between SCLK strings and ET or UTC">Converting between SCLK strings and ET or UTC</A>
         <A HREF="#Using encoded SCLK">Using encoded SCLK</A>
      <A HREF="#Encoded SCLK">Encoded SCLK</A>
         <A HREF="#Ticks">Ticks</A>
         <A HREF="#Partitions">Partitions</A>
      <A HREF="#SCLK Conversion Functions">SCLK Conversion Functions</A>
      <A HREF="#Distinguishing Between Different Clocks">Distinguishing Between Different Clocks</A>
         <A HREF="#Clock Types">Clock Types</A>
         <A HREF="#Clock type-specific functions">Clock type-specific functions</A>
         <A HREF="#Spacecraft-Specific Parameters">Spacecraft-Specific Parameters</A>
      <A HREF="#The SCLK Kernel File">The SCLK Kernel File</A>
         <A HREF="#Partition boundaries">Partition boundaries</A>
         <A HREF="#Clock type assignment">Clock type assignment</A>
         <A HREF="#Clock type-specific parameters">Clock type-specific parameters</A>
      <A HREF="#Expanding the system: What NAIF must do">Expanding the system: What NAIF must do</A>
      <A HREF="#An Example Using SCLK Functions">An Example Using SCLK Functions</A>
   <A HREF="#SCLK01">SCLK01</A>
      <A HREF="#Conforming spacecraft clocks">Conforming spacecraft clocks</A>
      <A HREF="#Type 1 SCLK format">Type 1 SCLK format</A>
         <A HREF="#Galileo SCLK format">Galileo SCLK format</A>
         <A HREF="#Mars Global Surveyor SCLK format">Mars Global Surveyor SCLK format</A>
         <A HREF="#Voyager SCLK clock format">Voyager SCLK clock format</A>
      <A HREF="#Type 1 SCLK conversion">Type 1 SCLK conversion</A>
         <A HREF="#Conversion algorithms">Conversion algorithms</A>
      <A HREF="#Type 1 SCLK functions">Type 1 SCLK functions</A>
      <A HREF="#The type 1 SCLK kernel file">The type 1 SCLK kernel file</A>
         <A HREF="#Kernel ID assignment">Kernel ID assignment</A>
         <A HREF="#Parallel time system code assignment">Parallel time system code assignment</A>
         <A HREF="#SCLK type assignment">SCLK type assignment</A>
         <A HREF="#Format constant assignments">Format constant assignments</A>
         <A HREF="#Time coefficients">Time coefficients</A>
         <A HREF="#Partition boundaries0">Partition boundaries</A>
         <A HREF="#Sample SCLK kernels">Sample SCLK kernels</A>
   <A HREF="#Appendix: Document Revision History">Appendix: Document Revision History</A>
         <A HREF="#May 27, 2010">May 27, 2010</A>
         <A HREF="#April 1, 2009">April 1, 2009</A>
         <A HREF="#March 02, 2008">March 02, 2008</A>
         <A HREF="#December 21, 2004">December 21, 2004</A>
         <A HREF="#February 2, 2004">February 2, 2004</A>
         <A HREF="#April 12, 1999">April 12, 1999</A>

</PRE>

<HR SIZE=3 NOSHADE>

<BR><BR>
<A NAME="SCLK Required Reading"></A>
<p align="right"><a href="#top"><small>Top</small></a></p>
<H1> SCLK Required Reading
</H1><HR SIZE=3 NOSHADE><P><BR><BR><BR>
   Last revised on 2010 MAY 27 by E. D. Wright.
<P>
 
<BR><BR>
<A NAME="Abstract"></A>
<p align="right"><a href="#top"><small>Top</small></a></p>
<H2> Abstract
</H2><HR ALIGN="LEFT" WIDTH=50% ><P><BR><BR>
   The SCLK system is the component of SPICE concerned with spacecraft
   clock correlation data.
<P>
 
<BR><BR>
<A NAME="Introduction"></A>
<p align="right"><a href="#top"><small>Top</small></a></p>
<H2> Introduction
</H2><HR ALIGN="LEFT" WIDTH=50% ><P><BR><BR>
   The spacecraft clock is the onboard time-keeping mechanism that triggers
   most spacecraft events, such as shuttering of a camera. Since telemetry
   data are downlinked with this clock's time attached to it, spacecraft
   clock time (SCLK--pronounced ``s-clock'') is the fundamental time
   measurement for referencing many spacecraft activities.
<P>
 
   It is natural, then, that SCLK have an important role in the CSPICE
   system. In fact, all C-kernel pointing data are referenced to SCLK.
   CSPICE contains functions to convert between SCLK and other standard
   time systems, such as Ephemeris Time (ET) and Universal Time Coordinated
   (UTC).
<P>
 
<BR><BR>
<A NAME="References"></A>
<p align="right"><a href="#top"><small>Top</small></a></p>
<H3> References
</H3><P><BR><BR>
<UL>
<TT>1.</TT> SFOC SIS ``SFOC-2-SYS-Any-TimeForms,'' 02/06/90.
<BR><BR></UL>
<BR><BR>
<A NAME="Support for New Missions"></A>
<p align="right"><a href="#top"><small>Top</small></a></p>
<H3> Support for New Missions
</H3><P><BR><BR>
   The suite of SCLK functions has been designed to easily accommodate
   future missions. A later section describes how the system might be
   easily expanded to incorporate new spacecraft clocks.
<P>
 
<BR><BR>
<A NAME="Detection of Non-native Text Files"></A>
<p align="right"><a href="#top"><small>Top</small></a></p>
<H3> Detection of Non-native Text Files
</H3><P><BR><BR>
   Starting with the N0057 release of the SPICE Toolkit (March, 2004) the
   SPICE data loading mechanism detects and prohibits loading text kernel
   files containing lines terminated with EOF character(s) non-native to
   the platform on which the Toolkit was compiled. If a non-native EOL
   terminator is detected in the first 132 characters of a text kernel, the
   execution is stopped and an error message is displayed. This feature
   does not work with files that are smaller that 132 bytes or have the
   first line longer that 132 characters.
<P>
 
<BR><BR>
<A NAME="The Basics"></A>
<p align="right"><a href="#top"><small>Top</small></a></p>
<H2> The Basics
</H2><HR ALIGN="LEFT" WIDTH=50% ><P><BR><BR>
   In this section, we present a minimal subset of facts about the CSPICE
   SCLK system that you can get by with and still use the system
   successfully.
<P>
 
<BR><BR>
<A NAME="SCLK rates"></A>
<p align="right"><a href="#top"><small>Top</small></a></p>
<H3> SCLK rates
</H3><P><BR><BR>
   Most of the complexity of dealing with SCLK time values arises from the
   fact that the rate at which any spacecraft clock runs varies over time.
   As a consequence, the relationship between SCLK and ET or UTC is not
   accurately described by a linear function; usually, a piecewise linear
   function is used to model this relationship.
<P>
 
   The mapping that models the relationship between SCLK and other time
   systems is updated as a mission progresses. While the change in the
   relationship between SCLK and other systems will usually be small, you
   should be aware that it exists; it may be a cause of discrepancies
   between results produced by different sets of software.
<P>
 
<BR><BR>
<A NAME="SCLK kernels"></A>
<p align="right"><a href="#top"><small>Top</small></a></p>
<H3> SCLK kernels
</H3><P><BR><BR>
   SCLK files conform to a flexible format called ``NAIF text kernel''
   format. The SPICE file identification word provided by itself on the
   first line of a text SCLK file is ``KPL/SCLK''. Both the NAIF text
   kernel format and SPICE file identification word are described in detail
   in the Kernel Required Reading document, <a href="../req/kernel.html">kernel.req</a>.
<P>
 
   To use any of the SCLK conversion functions, your program must first
   load a SCLK kernel file. The code fragment
<P>
 
<PRE>
   <a href="../cspice/furnsh_c.html">furnsh_c</a> ( &lt;name of the SCLK kernel file goes here&gt; );
</PRE>
   accomplishes this. You must supply the actual name of the kernel file
   you want to load.
<P>
 
   In addition, you will usually need to load a leapseconds kernel. For
   some missions, conversions between SCLK and ET will require that both an
   SCLK and a leapseconds kernel be loaded. The code fragment
<P>
 
<PRE>
   <a href="../cspice/furnsh_c.html">furnsh_c</a> ( &lt;name of the LEAPSECONDS kernel file goes here&gt; );
</PRE>
   loads a leapseconds kernel. Leapseconds kernels are described in the
   TIME required reading document, <a href="../req/time.html">time.req</a>.
<P>
 
   Normally, you will load these kernels at just one point in your
   application program, prior to using any time conversion functions.
<P>
 
   Details concerning the kernel pool are covered in the KERNEL required
   reading document, <a href="../req/kernel.html">kernel.req</a>.
<P>
 
<BR><BR>
<A NAME="Partitions, briefly"></A>
<p align="right"><a href="#top"><small>Top</small></a></p>
<H3> Partitions, briefly
</H3><P><BR><BR>
   The lifetime of each mission is divided into intervals called
   ``partitions.'' Partitions are time intervals during which the
   spacecraft clock advances continuously. Every time that a discontinuity
   in a spacecraft clock's readout values occurs, a new partition is
   started. Discontinuities may consist of positive jumps, in which the
   spacecraft clock's readout ``skips'' ahead, or negative jumps, in which
   the spacecraft clock regresses.
<P>
 
   The fact that a spacecraft clock may regress raises the possibility that
   the clock may give the same reading at two or more different times. For
   this reason, SCLK strings in CSPICE are prefaced with partition numbers.
<P>
 
   The partition number is a positive integer followed by a forward slash,
   for example
<P>
 
<PRE>
   4 /
</PRE>
   Any number of blanks are allowed on either side of the slash.
<P>
 
   An example of a Galileo SCLK string with a partition number is
<P>
 
<PRE>
   1/100007:76:1
</PRE>
   Partition numbers serve to ensure that spacecraft clock readings can be
   interpreted unambiguously.
<P>
 
<BR><BR>
<A NAME="Converting between SCLK strings and ET or UTC"></A>
<p align="right"><a href="#top"><small>Top</small></a></p>
<H3> Converting between SCLK strings and ET or UTC
</H3><P><BR><BR>
   The time known as ``spacecraft event time'' (SCET) is usually UTC. You
   must verify that this is the case for your spacecraft.
<P>
 
   To convert a SCLK string to a double precision ET value, you can use the
   function call
<P>
 
<PRE>
   <a href="../cspice/scs2e_c.html">scs2e_c</a> ( sc, clkstr, &amp;et  );
</PRE>
   To convert a SCLK string to a UTC string, you can use the code fragment
<P>
 
<PRE>
   <a href="../cspice/scs2e_c.html">scs2e_c</a>  ( sc, clkstr,         &amp;et );
   <a href="../cspice/timout_c.html">timout_c</a> ( et, pictur, lenout, utc );
</PRE>
   where
<P>
 
<DL><DT>
<B>
 `sc'
</B><BR><BR>
<DD>
 is the NAIF spacecraft ID code for your spacecraft.<BR>
</DL>
<DL><DT>
<B>
 `clkstr'
</B><BR><BR>
<DD>
 is a SCLK string.<BR>
</DL>
<DL><DT>
<B>
 `et'
</B><BR><BR>
<DD>
 is an ET time.<BR>
</DL>
<DL><DT>
<B>
 `pictur'
</B><BR><BR>
<DD>
 is a format picture for <a href="../cspice/timout_c.html">timout_c</a>.<BR>
</DL>
<DL><DT>
<B>
 `lenout'
</B><BR><BR>
<DD>
 is the output string length.<BR>
</DL>
<DL><DT>
<B>
 `utc'
</B><BR><BR>
<DD>
 is the UTC time equivalent to SCLK.<BR>
</DL>
   See these functions for details concerning their arguments.
<P>
 
   The inverse conversion is performed by the code fragment
<P>
 
<PRE>
   <a href="../cspice/str2et_c.html">str2et_c</a> ( utc, &amp;et                );
   <a href="../cspice/sce2s_c.html">sce2s_c</a>  ( sc,  et, lenout, clkstr );
</PRE>
<BR><BR>
<A NAME="Using encoded SCLK"></A>
<p align="right"><a href="#top"><small>Top</small></a></p>
<H3> Using encoded SCLK
</H3><P><BR><BR>
   The CSPICE C kernel (CK) system tags CK data with SCLK times. Within the
   CK system, these time tags are encoded as double precision numbers. To
   look up CK data, you will need to supply encoded SCLK time tags to the
   CK reader functions.
<P>
 
   You can obtain encoded SCLK values from SCLK strings via the function
   <a href="../cspice/scencd_c.html">scencd_c</a>. The code fragment
<P>
 
<PRE>
   <a href="../cspice/scencd_c.html">scencd_c</a> ( sc, clkstr, &amp;sclkdp );
</PRE>
   encodes the SCLK string `clkstr' as the double precision value `sclkdp'.
<P>
 
   Encoded SCLK values can be converted to strings using the code fragment
<P>
 
<PRE>
   <a href="../cspice/scdecd_c.html">scdecd_c</a> ( sc, sclkdp, lenout, clkstr );
</PRE>
   You can obtain continuous encoded SCLK values from ET via the function
   <a href="../cspice/sce2c_c.html">sce2c_c</a>. The code fragment
<P>
 
<PRE>
   <a href="../cspice/sce2c_c.html">sce2c_c</a> ( sc, et, &amp;sclkdp );
</PRE>
   encodes the ephemeris time ET as the double precision value `sclkdp'.
   SCLKDP need not be integral; even though non-integral tick values do not
   represent SCLK readings, they are permitted to avoid truncation error
   when representing ET as encoded SCLK.
<P>
 
   A parallel routine <a href="../cspice/sce2t_c.html">sce2t_c</a> converts ET to encoded SCLK, rounding the
   result to the nearest integral tick.
<P>
 
   The inverse conversion is provided by the routine <a href="../cspice/sct2e_c.html">sct2e_c</a>, which is
   called as follows:
<P>
 
<PRE>
   <a href="../cspice/sct2e_c.html">sct2e_c</a> ( sc, sclkdp, &amp;et );
</PRE>
   SCT2E handles integral or continuous tick values as inputs.
<P>
 
   There is a special function that is used for encoding ``tolerance''
   values for the CK readers. (See the CK Required Reading, <a href="../req/ck.html">ck.req</a>,
   document for a discussion of the CK readers.)
<P>
 
   The code fragment
<P>
 
<PRE>
   <a href="../cspice/sctiks_c.html">sctiks_c</a> ( sc, clkstr, &amp;ticks );
</PRE>
   produces an encoded tolerance value. <a href="../cspice/sctiks_c.html">sctiks_c</a> takes SCLK strings WITHOUT
   partition numbers as inputs; this is because the strings indicate a
   delta time rather than an absolute time.
<P>
 
   All of the concepts used in this section are discussed in greater detail
   in the following sections of this document.
<P>
 
<BR><BR>
<A NAME="Encoded SCLK"></A>
<p align="right"><a href="#top"><small>Top</small></a></p>
<H2> Encoded SCLK
</H2><HR ALIGN="LEFT" WIDTH=50% ><P><BR><BR>
   The fundamental representation of SCLK in the CSPICE system is a double
   precision numeric encoding of each multi-component count. Encoding SCLK
   provides the following advantages:
<P>
 
<UL>
<TT>--</TT> Encoding makes for a more compact representation. Direct (un-encoded)
representation of spacecraft clock counts usually requires multiple numbers
for the separate components making up the SCLK count.
<BR><BR></UL>
<UL>
<TT>--</TT> Having a single numeric equivalent for each count makes it much easier to
compare SCLK times (Is time t1 greater than time t2? Is time t1 closer to
time t2 than time t3? And so on.)
<BR><BR></UL>
   For these reasons, encoded SCLK is the time representation that is
   associated with pointing data in the C-kernel. Encoded SCLK is the basis
   by which conversions are made from SCLK to other time systems.
<P>
 
   To convert a character representation of an SCLK count `sclkch' to its
   double precision encoding `sclkdp', use the function <a href="../cspice/scencd_c.html">scencd_c</a> (Encode
   SCLK):
<P>
 
<PRE>
   <a href="../cspice/scencd_c.html">scencd_c</a> ( sc, sclkch, &amp;sclkdp );
</PRE>
   The function <a href="../cspice/scdecd_c.html">scdecd_c</a> (Decode SCLK) recovers the character
   representation of spacecraft clock from its double precision encoding.
<P>
 
<PRE>
   <a href="../cspice/scdecd_c.html">scdecd_c</a> ( sc, sclkdp, lenout, sclkch );
</PRE>
   The first argument to both functions, `sc', is the NAIF integer ID for
   the spacecraft whose clock count is being encoded or decoded (for
   example, --32 for Voyager 2). Each spacecraft may have a different
   format for its clock counts, so the encoding scheme may be different for
   each.
<P>
 
   Later chapters describing clock types give complete details on clock
   string formats for spacecraft clocks supported by the CSPICE Toolkit.
<P>
 
<BR><BR>
<A NAME="Ticks"></A>
<p align="right"><a href="#top"><small>Top</small></a></p>
<H3> Ticks
</H3><P><BR><BR>
   The units of encoded SCLK are ``ticks since spacecraft clock start,''
   where a ``tick'' is defined to be the shortest time increment
   expressible by a particular spacecraft's clock.
<P>
 
   An analogy can be drawn with a standard wall clock, showing hours,
   minutes, and seconds. One tick for a wall clock would be one second. And
   a wall clock time of
<P>
 
<PRE>
   10:05:50
</PRE>
   would represent
<P>
 
<PRE>
   10(3600) + 5(60) + 50 = 36350
</PRE>
   ticks.
<P>
 
   As in the case of the wall clock, the length of time associated with a
   tick varies as the clock rate varies.
<P>
 
   Since not all spacecraft clocks are the same, the particular time value
   for one tick varies from spacecraft to spacecraft. For Mars Global
   Surveyor, for instance, one tick is equivalent to approximately four
   milliseconds. For Galileo, it's about 8 1/3 milliseconds.
<P>
 
   In addition to representing spacecraft clock readings, ticks can be used
   to represent arbitrary epochs. In order to minimize discretization
   error, ``continuous'' (non-integral) tick values are supported:
   ephemeris times may be converted to non-integral ticks via the function
   <a href="../cspice/sce2c_c.html">sce2c_c</a>.
<P>
 
   Conversion of spacecraft clock strings to ticks always produces integral
   tick values.
<P>
 
<BR><BR>
<A NAME="Partitions"></A>
<p align="right"><a href="#top"><small>Top</small></a></p>
<H3> Partitions
</H3><P><BR><BR>
   One desirable feature of encoded SCLK is that it increases continuously
   throughout the course of the mission. Unfortunately, real spacecraft
   clocks do not always behave so nicely. A clock may reset to a lower
   value, rendering certain counts ambiguous. This might happen if the
   clock has reached its maximum expression, or because of a power surge. A
   clock may also jump ahead.
<P>
 
   Any time one of these discontinuities occurs, we say that SCLK time has
   entered a new partition. The partitions must be accounted for when
   encoding and decoding SCLK.
<P>
 
   To continue our analogy, say our wall clock was being used to keep time
   throughout an entire day. Then 10:05:50 is ambiguous, because we don't
   know if it falls in the morning or evening ``partition.'' So we append
   the indicators ``a.m.''\ or ``p.m.''\ to be clear.
<P>
 
   We handle SCLK similarly. Instead of just converting a clock count to
   ticks (10:05:50 to 36350), we take into account the partition that the
   count falls in, and compute the number of ticks since clock start
   (10:05:50 a.m. to 36350; 10:05:50 p.m. to 36350 + 12(60)(60) = 79550).
<P>
 
   When you pass a SCLK string to <a href="../cspice/scencd_c.html">scencd_c</a>, it is normally prefixed with a
   number indicating the partition in which the count falls. Sample SCLK
   strings for Voyager 2, including partition numbers, are given in an
   example program later in this document.
<P>
 
   The presence of the partition number is not always required. If it is
   missing, <a href="../cspice/scencd_c.html">scencd_c</a> will assume the partition to be the earliest one
   possible that contains the clock string being encoded. It's good
   practice to always include the partition number in SCLK strings.
<P>
 
   To convert to ticks since clock start, <a href="../cspice/scencd_c.html">scencd_c</a> processes the partition
   number. It has to know how many ticks were in all preceding partitions,
   and what the start and stop clock values were for each. This information
   is stored in a SCLK kernel file for that spacecraft. The SCLK kernel
   file is described in detail in a later section.
<P>
 
   New partitions may occur at any time throughout the course of active
   missions. The responsible mission operations team must update the SCLK
   kernel file to include new partitions as they occur.
<P>
 
   In converting encoded SCLK back to an equivalent clock string, <a href="../cspice/scdecd_c.html">scdecd_c</a>
   must also use the SCLK kernel file. Note, however, that you only have to
   load the SCLK kernel file once in your program, no matter how many calls
   to <a href="../cspice/scencd_c.html">scencd_c</a> and <a href="../cspice/scdecd_c.html">scdecd_c</a> are made afterwards. See the KERNEL required
   reading file, <a href="../req/kernel.html">kernel.req</a>, for information about ``loading''
   miscellaneous kernel files into the kernel pool.
<P>
 
   <a href="../cspice/scdecd_c.html">scdecd_c</a> always returns a clock string prefixed by a partition number
   and the '/' character, for example
<P>
 
<PRE>
   2/2000:83:12
</PRE>
   If you want to read partition start and stop times for yourself, use the
   function <a href="../cspice/scpart_c.html">scpart_c</a>:
<P>
 
<PRE>
   <a href="../cspice/scpart_c.html">scpart_c</a> ( sc, nparts, pstart, pstop );
</PRE>
<BR><BR>
<A NAME="SCLK Conversion Functions"></A>
<p align="right"><a href="#top"><small>Top</small></a></p>
<H2> SCLK Conversion Functions
</H2><HR ALIGN="LEFT" WIDTH=50% ><P><BR><BR>
   In order to correlate data obtained from different components of the
   CSPICE system, for example pointing and ephemeris data, it is necessary
   to be able to convert between SCLK time and representations of time in
   other systems, such as UTC and ephemeris time (also referred to as
   ``ET,'' ``barycentric dynamical time,'' and ``TDB'').
<P>
 
   CSPICE contains the following functions to convert between encoded and
   character SCLK, ET and UTC. Note that the names of the functions
   involving SCLK are all prefixed with `sc', for Spacecraft Clock.
<P>
 
<B><a href="../cspice/et2utc_c.html">et2utc_c</a></B>   (et, format, prec, lenout, utc)       (Convert ET to a
                                                        utc string)
</PRE>
<BR>
<B><a href="../cspice/utc2et_c.html">utc2et_c</a></B>   (utc, et)                             (Convert a utc
                                                        string to ET)
</PRE>
<BR>
<B><a href="../cspice/scencd_c.html">scencd_c</a></B>   (sc, sclkch, sclkdp)                  (Encode SCLK)
</PRE>
<BR>
<B><a href="../cspice/scdecd_c.html">scdecd_c</a></B>   (sc, sclkdp, lenout, sclkch)          (Decode SCLK)
</PRE>
<BR>
<B><a href="../cspice/sct2e_c.html">sct2e_c</a></B>    (sc, sclkdp, et)                      (Convert encoded
                                                        SCLK ticks to ET)
</PRE>
<BR>
<B><a href="../cspice/scs2e_c.html">scs2e_c</a></B>    (sc, sclkch, et)                      (Convert SCLK
                                                        string to ET)
</PRE>
<BR>
<B><a href="../cspice/sce2c_c.html">sce2c_c</a></B>    (sc, et, sclkdp)                      (Convert ET to
                                                        continuous ticks)
</PRE>
<BR>
<B><a href="../cspice/sce2t_c.html">sce2t_c</a></B>    (sc, et, sclkdp)                      (Convert ET to
                                                        encoded SCLK ticks)
</PRE>
<BR>
<B><a href="../cspice/sce2s_c.html">sce2s_c</a></B>    (sc, et, lenout, sclkch)              (Convert ET to SCLK
                                                        string)
</PRE>
<BR>
   It takes at most two function calls to convert between any two of the
   four representations.
<P>
 
   CSPICE also contains two functions that can encode and decode relative,
   or ``delta'' SCLK times. These are SCLK strings without partition
   numbers that represent time increments rather than total time since
   clock start. Such strings are encoded as tick counts. The functions are:
<P>
 
<B><a href="../cspice/sctiks_c.html">sctiks_c</a></B>   ( sc, clkstr, ticks )         (Convert delta SCLK to
                                                ticks )
</PRE>
<BR>
<B><a href="../cspice/scfmt_c.html">scfmt_c</a></B>    (sc, ticks, lenout, clkstr)   (Convert ticks to delta
                                                SCLK)
</PRE>
<BR>
<BR><BR>
<A NAME="Distinguishing Between Different Clocks"></A>
<p align="right"><a href="#top"><small>Top</small></a></p>
<H2> Distinguishing Between Different Clocks
</H2><HR ALIGN="LEFT" WIDTH=50% ><P><BR><BR>
   The algorithms used to encode and decode SCLK, and convert between SCLK
   and other time systems are not necessarily the same for each spacecraft.
<P>
 
   The differences are handled by the SCLK software at two levels:
   High-level differences are managed in the code itself through ``clock
   types.'' More detailed spacecraft-specific differences are handled using
   parameters in a SCLK kernel.
<P>
 
<BR><BR>
<A NAME="Clock Types"></A>
<p align="right"><a href="#top"><small>Top</small></a></p>
<H3> Clock Types
</H3><P><BR><BR>
   A clock type is a general clock description that may encompass several
   separate spacecraft clocks. Each clock type is identified in the SCLK
   functions by an integer code. At the release date of the current
   revision of this document, all supported missions use spacecraft clock
   type 1.
<P>
 
   A spacecraft clock data type has two components: a format defining the
   set of acceptable spacecraft clock (SCLK) strings, and a method of
   converting SCLK strings to a standard time representation, such as
   ephemeris or UTC seconds past J2000.
<P>
 
   For example, a type 1 clock consists of some number of cascading integer
   counters. An individual counter can increment only when the immediately
   preceding counter reaches its maximum expression and ``rolls over.'' Our
   wall clock is an example: the counters are hours, minutes and seconds.
   One tick for a type 1 clock is defined to be the value of the
   least-significant component increment. Clock type 1 uses a
   piecewise-linear interpolation process to convert between SCLK and other
   time systems.
<P>
 
   The chapter ``SLCK01'' describes clock type 1 in detail. It includes the
   specific SCLK string formats for each of the type 1 spacecraft clocks
   supported by the CSPICE Toolkit.
<P>
 
   SCLK functions determine the clock type for a particular spacecraft from
   the SCLK kernel file (described in the next section).
<P>
 
<BR><BR>
<A NAME="Clock type-specific functions"></A>
<p align="right"><a href="#top"><small>Top</small></a></p>
<H3> Clock type-specific functions
</H3><P><BR><BR>
   Each clock type is supported in the encoding and decoding process by the
   function sccc_c, where cc is the number of the clock type. sccc_c
   contains two entry points:
<P>
 
<B>sctkcc_</B>    (sc, clkstr, ticks, len_clkstr )   (SCLK string to ticks,
                                                     type cc)
</PRE>
<BR>
<B>scfmcc_</B>    (sc, ticks, clkstr, len_clkstr)    (Ticks to SCLK string,
                                                     type cc)
</PRE>
<BR>
   sctkcc_ and scfmcc_ do not process any partition information; that work
   is handled at a higher level by <a href="../cspice/scencd_c.html">scencd_c</a> and <a href="../cspice/scdecd_c.html">scdecd_c</a>, and is the same
   for all spacecraft clocks.
<P>
 
   sctkcc_ and scfmcc_ are called by <a href="../cspice/sctiks_c.html">sctiks_c</a> and <a href="../cspice/scfmt_c.html">scfmt_c</a>, respectively.
<P>
 
   Each clock type is supported in the time conversion process by two
   functions:
<P>
 
<B>sctecc_</B>   (sc, sclkdp, et)    (Encoded SCLK ticks to ET, type cc)
</PRE>
<BR>
<B>sceccc_</B>   (sc, et, sclkdp)    (ET to continuous ticks, type cc)
</PRE>
<BR>
<BR><BR>
<A NAME="Spacecraft-Specific Parameters"></A>
<p align="right"><a href="#top"><small>Top</small></a></p>
<H3> Spacecraft-Specific Parameters
</H3><P><BR><BR>
   Once the clock type has been determined, SCLK functions need parameters
   that uniquely distinguish each spacecraft within the same SCLK type. For
   instance, for type 1, they need to know: How many components make up
   this particular clock? What are the modulus values for each of the
   components? What are the coefficients defining the mapping from SCLK to
   a ``parallel'' time system, such as ET? Spacecraft-specific parameters
   such as these are read from the SCLK kernel file at run-time (see
   below).
<P>
 
<BR><BR>
<A NAME="The SCLK Kernel File"></A>
<p align="right"><a href="#top"><small>Top</small></a></p>
<H2> The SCLK Kernel File
</H2><HR ALIGN="LEFT" WIDTH=50% ><P><BR><BR>
   NAIF SCLK kernel files supply CSPICE SCLK conversion functions with
   information required to convert between SCLK values and other
   representations of time. Typically, a NAIF SCLK kernel will describe the
   clock of a single spacecraft.
<P>
 
   Before calling any of the functions to encode or decode SCLK, or convert
   between SCLK and other time systems, an application program must load
   the contents of the SCLK kernel file into the kernel pool, using the
   function <a href="../cspice/furnsh_c.html">furnsh_c</a> (load pool):
<P>
 
<PRE>
   <a href="../cspice/furnsh_c.html">furnsh_c</a> ( "name_of_SCLK_kernel_file" );
</PRE>
   An application must also load the leapseconds kernel file if there are
   any conversions to be performed between ET and UTC. This is typically
   done in the initialization section of your program.
<P>
 
   The SCLK kernel file you use should contain values for the particular
   spacecraft you are dealing with. The variables expected to be found in
   the file are all prefixed with the string
<P>
 
<PRE>
   SCLK_
</PRE>
   These variables include partition boundaries, clock type, and several
   other parameters associated with the clock type. These are described
   below.
<P>
 
<BR><BR>
<A NAME="Partition boundaries"></A>
<p align="right"><a href="#top"><small>Top</small></a></p>
<H3> Partition boundaries
</H3><P><BR><BR>
   The tick values for the beginning and end of each partition are given
   by:
<P>
 
<PRE>
   SCLK_PARTITION_START_ss = ( .....
                               .....
                               .....
                               ..... )
 
   SCLK_PARTITION_END_ss   = ( .....
                               .....
                               .....
                               ..... )
</PRE>
   where --ss is the spacecraft ID code. These variables are arrays
   containing one element per partition. The nth element of
<P>
 
<PRE>
   SCLK_PARTITITION_END_ss
</PRE>
   is considered to be the ``first tick'' of the (n+1)st partition.
   Mathematically speaking, partitions may be thought of as intervals that
   are closed on the left and open on the right.
<P>
 
<BR><BR>
<A NAME="Clock type assignment"></A>
<p align="right"><a href="#top"><small>Top</small></a></p>
<H3> Clock type assignment
</H3><P><BR><BR>
   If --ss is the NAIF ID code of a spacecraft, the associated clock type
   for that spacecraft is given by the assignment
<P>
 
<PRE>
   SCLK_DATA_TYPE_ss = ( cc )
</PRE>
   where cc is the clock type. New clock types will be developed as needed.
<P>
 
   Note that multiple spacecraft ID codes can be associated with the type 1
   SCLK data type at one time. Since the spacecraft codes are included in
   the SCLK variable names, there will be no naming conflicts. (We don't
   expect this feature to be used much, if at all, but it's there should
   you need it.)
<P>
 
<BR><BR>
<A NAME="Clock type-specific parameters"></A>
<p align="right"><a href="#top"><small>Top</small></a></p>
<H3> Clock type-specific parameters
</H3><P><BR><BR>
   Each spacecraft clock type has its own set of parameters that the CSPICE
   SCLK functions require in order to convert SCLK values of that type. A
   complete list and description of these parameters, and their variable
   names for the kernel pool, is given for type 1 in the chapter
   ``SCLK01.''
<P>
 
<BR><BR>
<A NAME="Expanding the system: What NAIF must do"></A>
<p align="right"><a href="#top"><small>Top</small></a></p>
<H2> Expanding the system: What NAIF must do
</H2><HR ALIGN="LEFT" WIDTH=50% ><P><BR><BR>
   Accommodating new spacecraft clocks may involve no code changes to the
   SCLK subroutines whatsoever.
<P>
 
   If a new clock fits into the framework of clock type 1, then the clock
   can be accommodated simply by producing a new kernel file for that
   spacecraft clock. For the new clock, a new set of kernel variables
   corresponding to those described above, and those in the chapter
   ``SCLK01,'' could be added to an existing SCLK kernel file.
   Alternatively, an entirely new SCLK kernel file containing the new
   parameters could be created --- this is the more likely approach. Once
   this is done, all existing SCLK functions will function, without
   modification, using the spacecraft ID.
<P>
 
   If a new clock does not fit into the clock type 1 framework, then NAIF
   will design a new clock type. This will involve writing new versions of
   the four clock type-specific functions described earlier:
<P>
 
<PRE>
   sctkcc_
   scfmcc_
   sctecc_
   sceccc_
</PRE>
   where cc is the new clock type number.
<P>
 
   New cases will have to be added to the code of the following
   higher-level SCxxx conversion functions to call the new, type-specific
   functions:
<P>
 
<PRE>
   <a href="../cspice/scfmt_c.html">scfmt_c</a>
   <a href="../cspice/sctiks_c.html">sctiks_c</a>
   <a href="../cspice/sct2e_c.html">sct2e_c</a>
   <a href="../cspice/scs2e_c.html">scs2e_c</a>
   <a href="../cspice/sce2c_c.html">sce2c_c</a>
   <a href="../cspice/sce2t_c.html">sce2t_c</a>
   <a href="../cspice/sce2s_c.html">sce2s_c</a>
</PRE>
   It will probably be necessary to design new SCLK kernel file variables
   to accommodate the new type, and augment the standard variables
   described above.
<P>
 
   Adding a new clock type does not change the calling sequence of any of
   the high-level conversion functions. Thus, once you've learned how to
   use the SCLK conversion functions, you won't have to re-learn just
   because a new spacecraft clock has been introduced.
<P>
 
<BR><BR>
<A NAME="An Example Using SCLK Functions"></A>
<p align="right"><a href="#top"><small>Top</small></a></p>
<H2> An Example Using SCLK Functions
</H2><HR ALIGN="LEFT" WIDTH=50% ><P><BR><BR>
   The following example shows how some of the SCLK functions might be used
   in a typical application program. This one reads pointing data from a
   C-kernel file. In this example, a set of four input clock times are
   hard-coded in the program for the purpose of demonstration: A real
   application written by you would likely get input times from some
   external source, such as a file or through interactive user input.
<P>
 
<PRE>
   /*
      Request pointing from a C-kernel file for a sequence of
      pictures obtained from the Voyager 2 narrow angle camera.
      Use an array of character spacecraft clock counts as input.
 
      Decode the output clock counts and print the input and
      output clock strings. Also print the equivalent UTC time
      for each output clock time.
 
      Note that the SCLK kernel file must contain VGR 2 clock
      information.
   */
 
 
   #include &lt;stdio.h&gt;
   #include "SpiceUsr.h"
 
   void main()
   {
 
      /*
      Local constants:
      */
      #define      NPICS     4
      #define      TIMLEN    25
      #define      LINLEN    80
 
      /*
      Names of C kernel and SCLK kernels:
      */
      #define      CK        "VGR2NA.BC"
      #define      SCLKKER   "SCLK.KER"
      #define      LSK       "LSK.KER"
 
      /*
      The instrument we want pointing for is the Voyager 2
      narrow angle camera.  The reference frame we want is
      J2000. The spacecraft is Voyager 2.
      */
      #define      INST      -32001
      #define      REF       "J2000"
      #define      SC        -32
 
 
      /*
      Local static variables:
      */
      static SpiceChar        clktol  [ TIMLEN ]  =  "0:01:001";
 
      static SpiceChar        sclkin  [ NPICS ] [ TIMLEN ]  =
                              {
                                 "2/20538:39:768",
                                 "2/20543:21:768",
                                 "2/20550:37",
                                 "2/20564:19"
                              };
 
      /*
      Local automatic variables:
      */
      SpiceBoolean            found;
 
      SpiceChar               sclkout [ TIMLEN ];
      SpiceChar               utc     [ TIMLEN ];
 
      SpiceDouble             cmat [3][3];
      SpiceDouble             et;
      SpiceDouble             timein;
      SpiceDouble             timeout;
      SpiceDouble             tol;
 
      SpiceInt                i;
      SpiceInt                sc;
 
 
      /*
      Load the appropriate files. We need
 
      1) A CK file containing pointing data.
      2) The SCLK kernel file, for the SCLK conversion functions.
      3) A leapseconds kernel, for ET-UTC conversions.
      */
 
      <a href="../cspice/furnsh_c.html">furnsh_c</a> ( CK,     );
      <a href="../cspice/furnsh_c.html">furnsh_c</a> ( SCLKKER );
      <a href="../cspice/furnsh_c.html">furnsh_c</a> ( LSK     );
 
 
      /*
      Convert the tolerance string to ticks.
      */
      <a href="../cspice/sctiks_c.html">sctiks_c</a> ( SC, clktol, &amp;tol );
 
      for ( i = 0;  i &lt; NPICS;  i++ )
      {
         <a href="../cspice/scencd_c.html">scencd_c</a> ( SC, sclkin[i], &amp;timein );
 
         <a href="../cspice/ckgp_c.html">ckgp_c</a>   ( INST,  timein, tol, REF, cmat, &amp;timeout,
                    &amp;found                                  );
 
         <a href="../cspice/scdecd_c.html">scdecd_c</a> ( SC, timeout, TIMLEN, sclkout     );
         <a href="../cspice/sct2e_c.html">sct2e_c</a>  ( SC, timeout, &amp;et                 );
         <a href="../cspice/et2utc_c.html">et2utc_c</a> ( et, "D",     3,      TIMLEN, utc );
 
 
         if ( found )
         {
            printf ( "\n"
                     "Input  s/c clock count: %s\n"
                     "Output s/c clock count: %s\n"
                     "Output UTC:             %s\n"
                     "Output C-Matrix:        \n"
                     "\n"
                     "%f\t %f\t %f\t\n"
                     "%f\t %f\t %f\t\n"
                     "%f\t %f\t %f\t\n"
                     "\n",
 
                     sclkin[i],
                     sclkout,
                     utc,
                     cmat[0][0], cmat[0][1], cmat[0][2],
                     cmat[1][0], cmat[1][1], cmat[1][2],
                     cmat[2][0], cmat[2][1], cmat[2][2]   );
         }
         else
         {
            printf ( "\n"
                     "Input  s/c clock count: %s\n"
                     "No pointing found.\n",
                     sclkin[i]                     );
         }
      }
   }
</PRE>
   The output from this program looks like this:
<P>
 
<PRE>
   Input  s/c clock count:  2 / 20538:39:768
   Output s/c clock count:  2/20538.39.768
   Output UTC:              79-186/21:50:23.000
   Output C-Matrix:  &lt;first C-matrix&gt;
 
   Input  s/c clock count:  2 / 20543:21:768
   Output s/c clock count:  2/20543.22.768
   Output UTC:              79-187/01:35:57.774
   Output C-Matrix:  &lt;second C-matrix&gt;
 
   Input  s/c clock count:  2 / 20550:37
   Output s/c clock count:  2/20550.36.768
   Output UTC:              79-187/07:23:57.774
   Output C-Matrix:  &lt;third C-matrix&gt;
 
   Input  s/c clock count:  2 / 20564:19
   Output s/c clock count:  2/20564.19.768
   Output UTC:              79-187/18:22:21.774
   Output C-Matrix:  &lt;fourth C-matrix&gt;
</PRE>
<BR><BR>
<A NAME="SCLK01"></A>
<p align="right"><a href="#top"><small>Top</small></a></p>
<H1> SCLK01
</H1><HR SIZE=3 NOSHADE><P><BR><BR><BR>
   This chapter describes the type 1 SCLK format and conversion algorithms
   in detail. Also, the SCLK formats for supported spacecraft whose clocks
   conform to the type 1 specification are described.
<P>
 
<BR><BR>
<A NAME="Conforming spacecraft clocks"></A>
<p align="right"><a href="#top"><small>Top</small></a></p>
<H2> Conforming spacecraft clocks
</H2><HR ALIGN="LEFT" WIDTH=50% ><P><BR><BR>
   The following spacecraft have SCLK formats that conform to the type 1
   specification:
<P>
 
<UL>
<TT>--</TT> Cassini
<BR><BR></UL>
<UL>
<TT>--</TT> Galileo Orbiter
<BR><BR></UL>
<UL>
<TT>--</TT> Mars Global Surveyor
<BR><BR></UL>
<UL>
<TT>--</TT> Mars Climate Orbiter
<BR><BR></UL>
<UL>
<TT>--</TT> Mars Polar Lander
<BR><BR></UL>
<UL>
<TT>--</TT> NEAR
<BR><BR></UL>
<UL>
<TT>--</TT> Stardust
<BR><BR></UL>
<UL>
<TT>--</TT> Voyager 1
<BR><BR></UL>
<UL>
<TT>--</TT> Voyager 2
<BR><BR></UL>
   The spacecraft clock encoding and conversion functionality described in
   this document is fully supported by the CSPICE Toolkit for these
   spacecraft.
<P>
 
<BR><BR>
<A NAME="Type 1 SCLK format"></A>
<p align="right"><a href="#top"><small>Top</small></a></p>
<H2> Type 1 SCLK format
</H2><HR ALIGN="LEFT" WIDTH=50% ><P><BR><BR>
   The first standard NAIF spacecraft clock data type has two components: a
   format defining the set of acceptable spacecraft clock (SCLK) strings,
   and a method of converting SCLK strings to any of a set of standard time
   systems such as TDT or TDB.
<P>
 
   Type 1 SCLK strings have the form
<P>
 
<PRE>
   pppp/&lt;time string&gt;
</PRE>
   where pppp is a partition number between 1 and 9999 inclusive, and
<P>
 
<PRE>
   &lt;time string&gt;
</PRE>
   is a time representation that conforms to the type 1 SCLK format. The
   partition specification (number and slash character) is optional; SCLK
   strings without partition numbers are assumed to refer to times in the
   first partition in which the specified clock count occurred. It's good
   practice to always include the partition number.
<P>
 
   An example of a type 1 SCLK string (for Galileo) is
<P>
 
<PRE>
   3 / 10110007:09:6:1
</PRE>
   The number ``3'' is the partition number, the slash is a delimiter, and
   the rest of the string is a ``time string.'' With this example in hand,
   we're ready to define the type 1 SCLK format.
<P>
 
   The partition number is a positive integer followed by a forward slash,
   for example
<P>
 
<PRE>
   4 /
</PRE>
   Zero or more blanks are allowed on either side of the slash.
<P>
 
   A type 1 SCLK time string consists of a series of one or more fields,
   each of which contains an integer. All fields but the leftmost are
   optional. The fields of a time string represent modular counts of time
   units. (A ``mod n'' count increments from zero to n-1, and then cycles
   back to zero.) The values for a given field may be offset by some fixed
   integer, so that they range from m to m+n, where m is non-negative. The
   moduli of the various fields are not necessarily the same. The time unit
   associated with a given field, multiplied by the modulus for that field,
   gives the time unit for next field to the left.
<P>
 
   For each field but the first, values may exceed the modulus for the
   field. For example, the modulus of the fourth field of a Galileo SCLK
   string is 8, but the digit ``9'' is allowed in that field. So
<P>
 
<PRE>
   0:0:0:9
</PRE>
   is a valid Galileo SCLK string and represents the same time as
<P>
 
<PRE>
   0:0:1:1
</PRE>
   On input to CSPICE functions, the fields of a type 1 SCLK string may be
   separated by any of the delimiter characters
<P>
 
<PRE>
   -  .  ,  :  &lt;blank&gt;
</PRE>
   On output from CSPICE functions, the delimiter characters will be those
   defined by a parameter in the SCLK kernel, described later.
<P>
 
   Consecutive delimiters containing no intervening digits are treated as
   if they delimit zero values.
<P>
 
   Note that all fields in time strings represent integers, not decimal
   fractions. So, the strings
<P>
 
<PRE>
   11000687:9
 
   11000687:90
</PRE>
   do not represent the same time value: in the former, the second field
   indicates a count of 9; in the latter, 90.
<P>
 
<BR><BR>
<A NAME="Galileo SCLK format"></A>
<p align="right"><a href="#top"><small>Top</small></a></p>
<H3> Galileo SCLK format
</H3><P><BR><BR>
   An example of a valid time string (without a partition number) for the
   Galileo spacecraft clock is:
<P>
 
<PRE>
   16777214:90:9:7
</PRE>
   Numbering the fields from left to right, the time units and moduli of
   the fields are:
<P>
 
<PRE>
      Field              Time unit              Modulus
      -----     ---------------------------     --------
        1       60 2/3   sec.                   16777215
        2          2/3   sec.  (666 2/3 ms)           91
        3          1/15  sec.  ( 66 2/3 ms)           10
        4          1/120 sec.  (  8 1/3 ms)            8
</PRE>
   Fields 1--4 are known as: ``Real time image count'' (RIM), ``mod 91
   count,'' ``mod 10 count'' or ``real time interrupt count'' (RTI), and
   ``mod 8 count.'' The values in all fields normally range from zero to
   the modulus of the field, minus one.
<P>
 
   The maximum time value that the Galileo spacecraft clock can represent
   (16777214:90:9:7) is approximately 32 years.
<P>
 
<BR><BR>
<A NAME="Mars Global Surveyor SCLK format"></A>
<p align="right"><a href="#top"><small>Top</small></a></p>
<H3> Mars Global Surveyor SCLK format
</H3><P><BR><BR>
   An example of a valid time string (without a partition number) for the
   Mars Global Surveyor spacecraft clock is:
<P>
 
<PRE>
   4294967295.255
</PRE>
   Numbering the fields from left to right, the time units and moduli of
   the fields are:
<P>
 
<PRE>
      Field           Time unit                Modulus
      -----     ----------------------       ----------
        1       approximately 1 sec.         4294967296
        2       1/256 sec.                   256
</PRE>
   Field 1 is known as the ``sclk_secs count.'' Field 2 is known as the
   ``sclk_fine word.'' The values in the first and second fields normally
   range from zero to the modulus of the field, minus 1.
<P>
 
   The maximum time value that the Mars Global Surveyor spacecraft clock
   can represent (4294967295.255) is approximately 136 years.
<P>
 
<BR><BR>
<A NAME="Voyager SCLK clock format"></A>
<p align="right"><a href="#top"><small>Top</small></a></p>
<H3> Voyager SCLK clock format
</H3><P><BR><BR>
   An example of a valid time string (without a partition number) for both
   the Voyager 1 and Voyager 2 spacecraft clocks is:
<P>
 
<PRE>
   65535.59.800
</PRE>
   Numbering the fields from left to right, the time units and moduli of
   the fields are:
<P>
 
<PRE>
      Field        Time unit              Modulus
      -----     ------------------       ---------
        1         2880    sec.             65536
        2           48    sec.                60
        3            0.06 sec.               800
</PRE>
   Fields 1--3 are known as: ``Mod 16 count'' (actually mod 2**16), ``mod
   60 count,'' and ``mod 800 count.'' The values in the first and second
   fields normally range from zero to the modulus of the field, minus 1.
   The range of the third field is from 1 to 800. The ``offset'' for the
   third field is 1, so values in this field normally range from 1 to 800
   rather than from 0 to 799; values above 800 are allowed and treated as
   described above.
<P>
 
   The maximum time value that the Voyager 1 and Voyager 2 spacecraft
   clocks can represent (65535:59:800) is approximately six years.
<P>
 
<BR><BR>
<A NAME="Type 1 SCLK conversion"></A>
<p align="right"><a href="#top"><small>Top</small></a></p>
<H2> Type 1 SCLK conversion
</H2><HR ALIGN="LEFT" WIDTH=50% ><P><BR><BR>
   CSPICE contains functions that convert between type 1 clock strings and
   the following representations of time:
<P>
 
<UL>
<TT>--</TT> ET (TDB)
<BR><BR></UL>
<UL>
<TT>--</TT> encoded SCLK
<BR><BR></UL>
   The functions that carry out these conversions are described above in
   the chapter ``SCLK Conversion Functions.''
<P>
 
   Since CSPICE also contains functions that convert between any of a
   variety of standard time systems, including ET, UTC, Terrestrial
   Dynamical Time (TDT), TAI, TDB Julian date, TDT Julian Date, and UTC
   Julian Date, conversion between SCLK strings and any other time system
   supported by CSPICE requires at most two function calls.
<P>
 
<BR><BR>
<A NAME="Conversion algorithms"></A>
<p align="right"><a href="#top"><small>Top</small></a></p>
<H3> Conversion algorithms
</H3><P><BR><BR>
   For every type 1 spacecraft clock, encoded SCLK values are converted to
   ephemeris time (TDB) as follows: first, encoded SCLK values are mapped
   to equivalent time values in a standard time system such as TDB or TDT.
   If the standard time system is not TDB, values from this system are
   mapped to TDB.
<P>
 
   The standard time system used for the conversion is referred to here and
   in the CSPICE SCLK functions as the ``parallel'' time system. Normally,
   the CSPICE Toolkit will use only one parallel time system for any given
   spacecraft clock.
<P>
 
   Conversion from TDB to encoded SCLK follows the reverse path: first, TDB
   values are converted, if necessary, to equivalent values in the parallel
   time system; next, those parallel time values are converted to encoded
   SCLK.
<P>
 
   For each type 1 spacecraft clock, encoded SCLK is related to the
   parallel time system for that clock by a piecewise linear function. The
   function is defined by a set of pairs of encoded SCLK values and
   corresponding values in the parallel time system, and by a set of
   ``rate'' values that apply to the intervals between the pairs of time
   values. The rate values give the rate at which ``parallel time''
   increases with respect to encoded SCLK time during the interval over
   which the rate applies. The rates in a type 1 SCLK kernel have units of
<P>
 
<PRE>
    parallel time system units
   ----------------------------
   most significant clock count
</PRE>
   The units of the currently supported parallel time systems TDT and TDB
   are seconds measured in those respective systems. So clock rates may be
   TDT or TDB seconds per most significant clock count. For example, for
   the GLL orbiter spacecraft clock, the rate unit is ``TDB seconds per
   RIM.''
<P>
 
   The specific method by which pairs of time values and rates are used to
   map encoded SCLK to parallel time values is explained in detail below.
   In the following discussion we'll use the name ``PARSYS'' to refer to
   the parallel time system. We'll use the name MSF to indicate the number
   of ticks per most significant SCLK field.
<P>
 
   We can represent the data that define the SCLK-to-PARSYS mapping as a
   set of ordered triples of encoded SCLK values (in units of ticks since
   spacecraft clock start), their equivalents in PARSYS time, and the rates
   corresponding to each pair of times:
<P>
 
<PRE>
   ( s/c_clock(1),  parsys(1),  rate(1) )
                     .
                     .
                     .
   ( s/c_clock(n),  parsys(n),  rate(n) )
</PRE>
   The mapping of SCLK values to PARSYS times is carried out as follows: If
   the sclk time ``clock'' satisfies
<P>
 
<PRE>
   sclk(i)  &lt;  clock  &lt;  sclk(i+1)
            -
</PRE>
   then the corresponding PARSYS time is
<P>
 
<PRE>
   parsys(i)  +    ( rate(i)/MSF )  *  ( clock - sclk(i) )
</PRE>
   If
<P>
 
<PRE>
   clock  &gt;  clock(n)
          -
</PRE>
   the formula still applies, with i = n.
<P>
 
   To convert PARSYS time values to SCLK, we use an analogous method. If
   ``time'' is the value to be converted, and
<P>
 
<PRE>
   parsys(i)  &lt;  time  &lt;  parsys(i+1)
              _
</PRE>
   then the corresponding continuous encoded SCLK value is
<P>
 
<PRE>
                   time -  parsys(i)
   sclk(i)    +    ----------------
                     rate(i)/MSF
</PRE>
   If
<P>
 
<PRE>
   time &gt;  parsys(n)
        -
</PRE>
   the formula still applies, with i = n.
<P>
 
   Note that this method will not handle rate values of 0 parallel time
   system units per tick.
<P>
 
   When the function described by the pairs of time values and rates is
   continuous, then all rates except for the last one are redundant, since
<P>
 
<PRE>
                    parsys(i+1) -  parsys(i)
   rate(i)/MSF  =   ------------------------
                     sclk(i+1)  -   sclk(i)
</PRE>
   If the mapping from encoded SCLK to the parallel time system is not
   continuous, then the mapping will not be strictly invertible: if an
   encoded SCLK value is mapped to a parallel time value, then mapping that
   parallel time value to encoded SCLK may not yield the original encoded
   SCLK value. However, the capability of supporting non-continuous
   mappings is provided in case it is needed to implement the mapping
   provided by a flight project.
<P>
 
   In order for CSPICE SCLK conversion functions to work, the information
   represented by the ordered triples described above must be loaded via
   the kernel pool. See the section ``The spacecraft clock kernel file''
   below for details.
<P>
 
<BR><BR>
<A NAME="Type 1 SCLK functions"></A>
<p align="right"><a href="#top"><small>Top</small></a></p>
<H2> Type 1 SCLK functions
</H2><HR ALIGN="LEFT" WIDTH=50% ><P><BR><BR>
   Type 1 SCLK functions are normally called by the higher-level SCLK
   functions <a href="../cspice/scencd_c.html">scencd_c</a>, <a href="../cspice/scdecd_c.html">scdecd_c</a>, scs2e_c, sct2e_c, <a href="../cspice/sce2c_c.html">sce2c_c</a>, <a href="../cspice/sce2t_c.html">sce2t_c</a>,
   <a href="../cspice/sce2s_c.html">sce2s_c</a>, sctiks_c, and <a href="../cspice/scfmt_c.html">scfmt_c</a>; you should not need to call these
   functions directly, though direct calls to these functions are not
   prohibited.
<P>
 
   The type 1 SCLK functions are
<P>
 
<B>scfm01_</B>   (sc, ticks, clkstr, len_clkstr)               (Convert
                                                               ticks to a
                                                               type 1 SCLK
                                                               string)
</PRE>
<BR>
<B>sctk01_</B>   (sc, clkstr, ticks, len_clkstr)               (Convert a
                                                               type 1 SCLK
                                                               string to
                                                               ticks)
</PRE>
<BR>
<B>scec01_</B>   (sc, et, sclkdp)                              (ET to
                                                               continuous
                                                               ticks, type
                                                               1)
</PRE>
<BR>
<B>scet01_</B>   (sc, et, sclkdp)                              (Convert ET
                                                               to ticks,
                                                               type 1)
</PRE>
<BR>
<B>scte01_</B>   (sc, sclkdp, et)                              (Convert
                                                               ticks to ET,
                                                               type 1)
</PRE>
<BR>
<B>scld01_</B>   (name, sc, maxnv, n, dval)                    (SCLK look
                                                               up of double
                                                               precision
                                                               data, type
                                                               1)
</PRE>
<BR>
<B>scli01_</B>   (name, sc, maxnv, n, ival)                    (SCLK look
                                                               up of
                                                               integer
                                                               data, type
                                                               1)
</PRE>
<BR>
<B>sclu01_</B>   (name, sc, maxnv, n, ival, dval)              (SCLK
                                                               lookup, type
                                                               1)
</PRE>
<BR>
<B>sc01_</B>     (sc, clkstr, ticks, sclkdp, et, len_clkstr)   (SCLK
                                                               conversion,
                                                               type 1)
</PRE>
<BR>
   The last two functions sc01_ and sclu01_ are ``umbrella'' functions
   which exist for the purpose of allowing their entry points to share
   data. These functions should not be called directly.
<P>
 
<BR><BR>
<A NAME="The type 1 SCLK kernel file"></A>
<p align="right"><a href="#top"><small>Top</small></a></p>
<H2> The type 1 SCLK kernel file
</H2><HR ALIGN="LEFT" WIDTH=50% ><P><BR><BR>
   Before any CSPICE functions that make use of type 1 SCLK values can be
   used, a SCLK kernel file must be loaded into the kernel pool. Regardless
   of the clock type, an SCLK kernel assigns values to variables that
   define:
<P>
 
<UL>
<TT>--</TT> The clock type for a spacecraft
<BR><BR></UL>
<UL>
<TT>--</TT> The format of SCLK strings, for one or more spacecraft.
<BR><BR></UL>
<UL>
<TT>--</TT> The mapping between encoded SCLK values and a parallel time system.
<BR><BR></UL>
   Variables that are used for all clock types have names that start with
   the string
<P>
 
<PRE>
   SCLK_
</PRE>
   Variables that are applicable only to type 1 spacecraft clocks start
   with the string
<P>
 
<PRE>
   SCLK01_
</PRE>
   An SCLK kernel file makes the following assignments for each spacecraft
   whose clock values are to be treated as ``type 1'' by the CSPICE SCLK
   functions:
<P>
 
<BR><BR>
<A NAME="Kernel ID assignment"></A>
<p align="right"><a href="#top"><small>Top</small></a></p>
<H3> Kernel ID assignment
</H3><P><BR><BR>
   Each SCLK kernel must assign a identifier to the kernel variable
<P>
 
<PRE>
   SCLK_KERNEL_ID
</PRE>
   This identifier is normally a UTC time string, preceded by the character
   '@', for example,
<P>
 
<PRE>
   @04-SEP-1990
</PRE>
   If you have loaded multiple SCLK kernels into the kernel pool, the
   identifiers for these kernels should be distinct.
<P>
 
<BR><BR>
<A NAME="Parallel time system code assignment"></A>
<p align="right"><a href="#top"><small>Top</small></a></p>
<H3> Parallel time system code assignment
</H3><P><BR><BR>
   If --ss is the NAIF ID code of a spacecraft, this ID is associated with
   a parallel time system by the assignment
<P>
 
<PRE>
   SCLK01_TIME_SYSTEM_ss  = ( nnn )
</PRE>
   where nnn is a numeric code designating the time system that the
   coefficients in the kernel map encoded SCLK to. The time systems and
   codes currently in use are:
<P>
 
<DL><DT>
<B>
 Barycentric dynamical time (TDB)
</B><BR><BR>
<DD>
 1<BR>
</DL>
<DL><DT>
<B>
 Terrestrial dynamical time (TDT)
</B><BR><BR>
<DD>
 2<BR>
</DL>
   This assignment is optional; if absent, the parallel time system is
   assumed to be barycentric dynamical time.
<P>
 
<BR><BR>
<A NAME="SCLK type assignment"></A>
<p align="right"><a href="#top"><small>Top</small></a></p>
<H3> SCLK type assignment
</H3><P><BR><BR>
   If --ss is the NAIF ID code of a spacecraft, this ID is associated with
   a SCLK type by the assignment
<P>
 
<PRE>
   SCLK_DATA_TYPE_ss = ( 1 )
</PRE>
   Note that multiple mission ID codes can be associated with the type 1
   SCLK data type at one time. Since the mission codes are included in the
   SCLK variable names, there will be no naming conflicts.
<P>
 
<BR><BR>
<A NAME="Format constant assignments"></A>
<p align="right"><a href="#top"><small>Top</small></a></p>
<H3> Format constant assignments
</H3><P><BR><BR>
   All of the format constants start with the string
<P>
 
<PRE>
   SCLK01
</PRE>
   and end with the string
<P>
 
<PRE>
   _ss
</PRE>
   where --ss is the NAIF mission ID code. This allows the type 1 SCLK
   functions to find the correct constants for each mission ID associated
   with the first SCLK data type.
<P>
 
   The format constants that must be assigned are
<P>
 
<PRE>
   SCLK01_N_FIELDS_ss
   SCLK01_MODULI_ss
   SCLK01_OFFSETS_ss
   SCLK01_OUTPUT_DELIM_ss
</PRE>
   Here are sample assignments of values to the variables describing the
   format of type 1 SCLK strings. The values shown apply to the Galileo
   SCLK format.
<P>
 
   Number of fields:
<P>
 
<PRE>
   SCLK01_N_FIELDS_77  =  ( 4 )
</PRE>
   Modulus of each field:
<P>
 
<PRE>
   SCLK01_MODULI_77  =  ( 16777215 91 10 8 )
</PRE>
   Offsets for field values. Offsets are listed for each field in
   left-to-right order:
<P>
 
<PRE>
   SCLK01_OFFSETS_77 = ( 0 0 0 0 )
</PRE>
   Code for delimiter to be used in output strings. The codes and
   corresponding delimiters are:
<P>
 
<PRE>
   Code          Delimiter
 
     1               .
 
     2               :
 
     3               -
 
     4               ,
 
     5             &lt;space&gt;
</PRE>
   For Galileo, the code assignment would be:
<P>
 
<PRE>
   SCLK01_OUTPUT_DELIM_77 = ( 2 )
</PRE>
<BR><BR>
<A NAME="Time coefficients"></A>
<p align="right"><a href="#top"><small>Top</small></a></p>
<H3> Time coefficients
</H3><P><BR><BR>
   The data that define the mapping between SCLK and the parallel time
   system are called ``time coefficients.'' This name is used because the
   data are coefficients of linear polynomials; as a set, they define a
   piecewise linear function that maps SCLK to the parallel time system.
<P>
 
   The time coefficients are assigned to the variable
<P>
 
<PRE>
   SCLK01_COEFFICIENTS_ss
</PRE>
   where --ss is the spacecraft ID code. The assigned values are triplets
   of SCLK values, corresponding parallel time values, and rates. The SCLK
   values are expressed in total ticks since clock start. The parallel time
   values may be expressed in a variety of units. The rate values have
   units that depend on the units used for the parallel time values: if we
   call these units
<P>
 
<PRE>
   PARALLEL_TIME_UNITS
</PRE>
   then the rate units are
<P>
 
<PRE>
      PARALLEL_TIME_UNITS
   ----------------------------
   most significant clock count
</PRE>
   The term most ``significant clock count'' shown in the denominator
   refers to the length of time associated with one count of the most
   significant (leftmost) field of the formatted spacecraft clock string.
   For example, for Voyager 2, the most significant field of a formatted
   SCLK string is the ``mod 16'' field. For Galileo, the most significant
   field is the ``RIM count.'' For Mars Global Surveyor, the most
   significant field is the ``sclk_secs count.''
<P>
 
<BR><BR>
<A NAME="Partition boundaries0"></A>
<p align="right"><a href="#top"><small>Top</small></a></p>
<H3> Partition boundaries
</H3><P><BR><BR>
   In order to convert between SCLK strings and their encoded form of ticks
   since spacecraft clock start, it is necessary to know the initial and
   final SCLK readouts for each partition. These values are given by:
<P>
 
<PRE>
   PARTITION_START_ss
   PARTITION_END_ss
</PRE>
   where --ss is the spacecraft ID code. These variables are arrays
   containing one element per partition.
<P>
 
<BR><BR>
<A NAME="Sample SCLK kernels"></A>
<p align="right"><a href="#top"><small>Top</small></a></p>
<H3> Sample SCLK kernels
</H3><P><BR><BR>
   The following is a sample SCLK kernel for Galileo:
<P>
 
<PRE>
   KPL/SCLK
 
   \begindata
   SCLK_KERNEL_ID            = ( @04-SEP-1990//4:23:00 )
 
   SCLK_DATA_TYPE_77         = ( 1                )
   SCLK01_N_FIELDS_77        = ( 4                )
   SCLK01_MODULI_77          = ( 16777215 91 10 8 )
   SCLK01_OFFSETS_77         = (        0  0  0 0 )
   SCLK01_OUTPUT_DELIM_77    = ( 2                )
 
   SCLK_PARTITION_START_77   = ( 0.0000000000000E+00
                                 2.5465440000000E+07
                                 7.2800001000000E+07
                                 1.3176800000000E+08 )
 
   SCLK_PARTITION_END_77      = ( 2.5465440000000E+07
                                 7.2800000000000E+07
                                 1.3176800000000E+08
                                 1.2213812519900E+11 )
 
   SCLK01_COEFFICIENTS_77    = (
 
   0.0000000000000E+00  -3.2287591517365E+08  6.0666283888000E+01
   7.2800000000000E+05  -3.2286984854565E+08  6.0666283888000E+01
   1.2365520000000E+06  -3.2286561063865E+08  6.0666283888000E+01
   1.2365600000000E+06  -3.2286558910065E+08  6.0697000438000E+01
   1.2368000000000E+06  -3.2286557090665E+08  6.0666283333000E+01
   1.2962400000000E+06  -3.2286507557565E+08  6.0666283333000E+01
   2.3296480000000E+07  -3.2286507491065E+08  6.0666300000000E+01
   2.3519280000000E+07  -3.2286321825465E+08  5.8238483608000E+02
   2.3519760000000E+07  -3.2286317985565E+08  6.0666272281000E+01
   2.4024000000000E+07  -3.2285897788265E+08  6.0666271175000E+01
   2.5378080000000E+07  -3.2284769395665E+08  6.0808150200000E+01
   2.5421760000000E+07  -3.2284732910765E+08  6.0666628073000E+01
   2.5465440000000E+07  -3.2284696510765E+08  6.0666628073000E+01
   3.6400000000000E+07  -3.2275584383265E+08  6.0666627957000E+01
   7.2800000000000E+07  -3.2245251069264E+08  6.0666628004000E+01
   1.0919999900000E+08  -3.2214917755262E+08  6.0666628004000E+01
   1.2769119900000E+08  -3.2199508431761E+08  6.0665620197000E+01
   1.3085799900000E+08  -3.2196869477261E+08  6.0666892494000E+01
   1.3176799900000E+08  -3.2196111141061E+08  6.0666722113000E+01
   1.3395199900000E+08  -3.2194291139361E+08  6.0666674091000E+01
   1.3613599900000E+08  -3.2192471139161E+08  6.0666590261000E+01
   1.4341599900000E+08  -3.2186404480160E+08  6.0666611658000E+01
   1.5069599900000E+08  -3.2180337818960E+08  6.0666611658000E+01
   1.7253599900000E+08  -3.2162137835458E+08  6.0666783566000E+01
   1.7515679900000E+08  -3.2159953831258E+08  6.0666629213000E+01
   1.7777759900000E+08  -3.2157769832557E+08  6.0666629213000E+01
   3.3451599900000E+08  -3.2027154579839E+08  6.0666505193000E+01
   3.3713679900000E+08  -3.2024970585638E+08  6.0666627480000E+01
   3.3975759900000E+08  -3.2022786587038E+08  6.0666627480000E+01
   5.6601999900000E+08  -3.1834234708794E+08  6.0666396876000E+01
   5.6733039900000E+08  -3.1833142713693E+08  6.0666626282000E+01
   5.6864079900000E+08  -3.1832050714393E+08  6.0666626282000E+01
   8.9797999900000E+08  -3.1557601563707E+08  5.9666626282000E+01
   8.9798727900000E+08  -3.1557595597007E+08  6.0666626282000E+01
   8.9799455900000E+08  -3.1557589430307E+08  6.0666626282000E+01 )
 
   \begintext
</PRE>
   Below is a sample SCLK kernel file for Mars Global Surveyor. Note that
   the text prior to the first
<P>
 
<PRE>
   \begindata
</PRE>
   directive is treated as a group of comment lines by the SPICELIB kernel
   readers. The labels shown in this comment area are examples and should
   not be construed as a correct specification.
<P>
 
<PRE>
   KPL/SCLK
 
   Status
   -----------------------------------------------
 
      This file is a SPICE spacecraft clock (SCLK) kernel containing
      information required for Mars Global Surveyor spacecraft
      on-board clock to ET conversion.
 
 
   Production/History of this SCLK files
   -----------------------------------------------
 
      This file was generated by the NAIF utility program MAKCLK,
      version 3.3, from the most recent Mars Global Surveyor
      spacecraft SCLK SCET file.
 
 
   Usage
   -----------------------------------------------
 
      This file must be loaded into the user's program by a call to
      the FURNSH subroutine
 
            CALL FURNSH( 'this_file_name' )
 
      in order to use the SPICELIB SCLK family of subroutines to
      convert MGS spacecraft on-board clock to ET and vice versa and
      to use MGS frames defined below as reference frames for
      geometric quantities being returned by high-level SPK and
      CK subroutines.
 
 
   References
   -----------------------------------------------
 
      1. SCLK Required Reading file (<a href="../req/sclk.html">sclk.req</a>), NAIF document number 222
      2. MAKCLK User's Guide, NAIF document number 267
 
 
   Inquiries
   -----------------------------------------------
 
      If you have any questions regarding this file contact
 
      MGS Spacecraft Operations Team (SCOPS)
      Lockheed/Martin, Denver
 
      Boris Semenov - NAIF/JPL
      (818) 354-8136
      bsemenov@spice.jpl.nasa.gov
 
 
   SCLK DATA
   -----------------------------------------------
 
   \begindata
 
   SCLK_KERNEL_ID           = ( @1999-02-07/03:51:29.00 )
 
   SCLK_DATA_TYPE_94        = ( 1 )
   SCLK01_TIME_SYSTEM_94    = ( 2 )
   SCLK01_N_FIELDS_94       = ( 2 )
   SCLK01_MODULI_94         = ( 4294967296 256 )
   SCLK01_OFFSETS_94        = ( 0 0 )
   SCLK01_OUTPUT_DELIM_94   = ( 1 )
 
   SCLK_PARTITION_START_94  = ( 1.3611133440000E+11 )
 
   SCLK_PARTITION_END_94    = ( 1.0995116277750E+12 )
 
   SCLK01_COEFFICIENTS_94   = (
 
    0.0000000000000E+00  -9.9510252675000E+07  9.9999996301748E-01
    8.3066265600000E+08  -9.6265476795000E+07  9.9999994844682E-01
    1.9330583040000E+09  -9.1959244017000E+07  9.9999994927604E-01
    2.7708477440000E+09  -8.8686629183000E+07  9.9999994213351E-01
    4.0538009600000E+09  -8.3675093473000E+07  9.9999993609973E-01
    4.7829370880000E+09  -8.0826905655000E+07  9.9999993275158E-01
    5.2473643520000E+09  -7.9012736777000E+07  9.9999993064539E-01
    5.4909818880000E+09  -7.8061105843000E+07  9.9999992770059E-01
    6.7515176960000E+09  -7.3137138199000E+07  9.9999992410889E-01
    7.9017973760000E+09  -6.8643858540000E+07  9.9999992038548E-01
    8.9854187520000E+09  -6.4410962877000E+07  9.9999991689249E-01
    9.9588085760000E+09  -6.0608659193000E+07  9.9999991330346E-01
    1.1222619136000E+10  -5.5671899621000E+07  9.9999990916047E-01
    1.2448517120000E+10  -5.0883236056000E+07  9.9999990447344E-01
    1.3831336704000E+10  -4.5481597572000E+07  9.9999990051645E-01
    1.5223486464000E+10  -4.0043513113000E+07  9.9999989497162E-01
    1.7390367488000E+10  -3.1579135002000E+07  9.9999988993180E-01
    1.7567130624000E+10  -3.0888654078000E+07  9.9999989100000E-01 )
   \begintext
</PRE>
<BR><BR>
<A NAME="Appendix: Document Revision History"></A>
<p align="right"><a href="#top"><small>Top</small></a></p>
<H1> Appendix: Document Revision History
</H1><HR SIZE=3 NOSHADE><P><BR><BR><BR>
<BR><BR>
<A NAME="May 27, 2010"></A>
<p align="right"><a href="#top"><small>Top</small></a></p>
<H3> May 27, 2010
</H3><P><BR><BR>
   Minor edit to eliminate typo.
<P>
 
<BR><BR>
<A NAME="April 1, 2009"></A>
<p align="right"><a href="#top"><small>Top</small></a></p>
<H3> April 1, 2009
</H3><P><BR><BR>
   Added a note about the SPICE file identification word for SCLK files.
<P>
 
<BR><BR>
<A NAME="March 02, 2008"></A>
<p align="right"><a href="#top"><small>Top</small></a></p>
<H3> March 02, 2008
</H3><P><BR><BR>
   Updated discussion of type 1 conversion algorithm to clarify role of
   parallel time system. Updated discussion of SCLK string formats to
   indicate support for 4-digit partition numbers.
<P>
 
<BR><BR>
<A NAME="December 21, 2004"></A>
<p align="right"><a href="#top"><small>Top</small></a></p>
<H3> December 21, 2004
</H3><P><BR><BR>
   Added note regarding detection of non-native text files. Replaced
   <a href="../cspice/ldpool_c.html">ldpool_c</a> with <a href="../cspice/furnsh_c.html">furnsh_c</a>.
<P>
 
<BR><BR>
<A NAME="February 2, 2004"></A>
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<H3> February 2, 2004
</H3><P><BR><BR>
   Performed a spell-check on text.
<P>
 
<BR><BR>
<A NAME="April 12, 1999"></A>
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<H3> April 12, 1999
</H3><P><BR><BR>
   The document differs from the previous version of April 20, 1992 in that
   it documents the new capability of the SCLK software to convert between
   ET and continuous ticks. Examples involving Mars Observer have been
   updated to refer to Mars Global Surveyor. The quotation style has been
   changed from British to American. The program example showing use of the
   SCLK system together with the CK reader CKGP has been corrected.
   Miscellaneous minor changes of wording have been made throughout the
   text.
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